Method and apparatus for testing networks



Oct. 22,' 1929.- II-LNYQUIST 1,732,311

METHOD AND APP RATUS FQR TESTING NETWORKS Filed Feb. 25, 1926 2 Sheets-Sheet 1 IN VEN TOR 2y, 5 JZ MM A TTORNE Y Oct. 22, I929. I H. NYQUIST METHOD AND APPARATUSEEFOR TESTIRG.; NETWORKS Filed Febf 25, 1926* 2 Sheets-Sheet 2 nun vvvvvvvv rvvvvvvn AAAAAAAAA IN VEN TOR pared Patented 0a. 22 1929 UNITED STATES PATENT OFFICE.

HARRY NYQUIST, 0F MILLBURN, JERSEY, ASSIGNOR TO AMERICAN TELEPHONE I AND TELEGRAPH COMPANY, A CORPORATION OF NEW YORK METHOD AND APPARATUS FOR TESTING NETWORKS Application filed February 25, 1926. Serial No. 90,654.

An object of my invention is to provide a new and improved method and suitable apparatus for testing networks for the constant K relation. As will be explained here in, a constant K network has the property that if terminated on the output side by a resistance K, then its input impedance at all frequencies will be the constant resistance K. Constant K networks are useful for such applications as attenuation equalizers, phase compensators, delay networks, etc. It may be easier to design a network having a constant resistance for all frequencies as comwith a network having its resistance avariable function of frequency; also it will often be preferable to have the resistance constant so that there will be no discrimination among frequencies in'this respect. A constant K network can be interposed in a line whose characteristic impedance is the resistance K without producing reflection effects. Another object of my .invention relates to testing such a network without disassembling its elements. These and other objects of my invention will become apparent on consideration of a limited number of specific examples ofv practice according to the invention which I have chosen to disclose in this specification. It will be understood that the invention is defined in the appended claims and that the following description relates to these examples of the invention.

Referring to the drawings, Figure 1 i's a diagram of a certain constant K network;

Fig. 1 shows certain elements of this network arranged in abridge for testing the constantK relation; Fig. 2 shows how one kind of test maybe made without disasfor testing a constant K network for certain other constants; Fig. 4 shows a method for measuring impedances of parts of the network without disassembly thereof; Fig. 5 shows a bridgemethod in which uncompensated transformers are employed; Fig. 5

shows a network equivalent to that in Fig. 1 and of the same type as incorporated in Fig. 5; Fig. 6 shows equivalent T networks substituted for the transformers of Fig. 5;

the network; Fig. 3 shows a method Fig. 6 shows these equivalent T networks consolidated to one equivalent T network; Fig. 7 shows the substitution of resistances for the transformers of Fig. 5 in their aspect from another arm of the bridge of Fig. 5; Fig. 8 shows the proper compensating resistance introduced as compared with Fig. I

'6; Fig. 9 shows the proper compensating volved in my invention.

Referring to the network of Fig. 1 with the two input terminals A, A and the two output terminals B, B, it can easily be proved thatif Z is the impedance of the combination L, C and if Z is the impedance of the combination Z, 0, and if Z Z =K where K is a constant, then if the output terminals are connected with a resistance of value K the input impedance will be the resistance K for all frequencies. Accordingly this network is an example of a constant K network.

It can also be shown that if the signal transmission delay through such a net work is plotted against frequency, the plots will have the character shown in Fig. 12 where b' is a parameter of design that determines the shape of the characteristic.

The nature and significance of this param *eter b and certain essential relations in which it is involved will be discussed in connection with the equations given hereinafter. To test the network of Fig. 1 for the con 'stant K relation, the bridge of Fig. 1 is ar ranged with the equal resistances K in one pair of opposite arms and with one combination L, C and one combination Z, a, respectively,1n the arms of the other pa1r. If an alternating current of varying frequency is applied across the bridge terminals, as indieated by E, and if theeflect is nullin the receiver Be at all the frequenciesof the desired range, and if the same is true for the remaining combinations L, C and Z, c, then it proves that the network has the constant K relation for that range.

If a balance is not obtained with the arrangement shown in Fig. 1*, it is possible to adjust either resistance and any one of the reactance elements until a balance is obtained. The characteristic impedance of the network section will then be equal to the square root of the product of the two resistance arms. Another method of adjustment to obtain a balance is to adjust two of the reactance elements, and this will'be preferable when it is desired not to alter the characteristic impedance of the network. In this case the two reactance elements chosen for adjustment should not consist of an inductance in one arm of the bridge and a capacity in the other arm,

because in that case it will not, in general, be possible to obtain a balance. The choice of any other pair of elements will make it possible to get a'balance.

In the case of Fig. 2, the network of Fig.' 1 is incorporated as a whole, and its parts are not separated as is the case in Fig. 1 The ,source E is of complex frequency, a voice- I work between the input terminals A, A and the output terminals B, B is, indeed, a constantK network, it will present a constant input impedance which is the'resistance K at all frequencies so that there will be a balance to the receiver he, and no sound will be heard. in it.

If the balance is not perfect, two reactance elements in the network may be altered (subject to the same restriction against an inductance in one member and a capacity in the other, as mentioned before) until a balance is obtained, or one reactance element can be ad justed, and at thesame time the two resistance elements K must be adjusted alike.

Whereas in Fig. 1 the adjustment for various frequencies was made by varying the frequencyof the source E, in Fig. 2 the-various frequencies are obtained by employing a composite electromotive source in which a yariety of frequencies are superposed. Fig. 2

not only relieves the operator from disassembling the network, but it also tests whether the section is properly put together, for example, whether it is wired correctly.

In Fig. 3 thenetwork isbalanced against an adjustable resistance R, and a switch S is provided by which the output terminals of the network can be directly connected or left open. When the switch S is closed, this puts L, C and Z, 0 in parallel, and such combination in series with a like combination. The baltion Z, 0, and the remaining combinations are likewise put in series, and the two series in parallel. Again adjustment is made of frequency and resistance R until balance is obtained'for a minimum value of resistance.

This will occur at two different frequencies which correspond to a quarter wave length in the section, that is, at the two frequencies 7", and f, for which the the section is 90.

phase shift in traversing Equations will now be deduced which are useful in computing the parameters of the network, when f, and f, have been found. Let the net-work be of the lattice form such as illustrated in Figure 1. It has been established (see, for example, Equations 23' on page 19 of Theory and design of uniform and composite electric wave-filters, by Otto J. Zobel, in- The'Bell System Technical J ournal, January, 1923) that and K: v Z122 Where I is the propagation constant per section K is the characteristic impedance z, is twice the impedance of the combination L, C z, is one-half the impedance of the Let two constants b and f be defined such that 5'0 the important parameters f and b.

Fig. 4 shows an arrangement which not Then When there is dissipation in the coils and condensers of the network this expression is usually found to be a satisfactory approximation. When ,3 is 90 at the frequency f,,

Whence,

2/?) f0/f1 f1/jo- When B is 90 at the frequency f,, a similar line of reasoning gives 7 f2/fofo/f2 Equating the right-hand members of the last two equations and solving for f 0 1 m Substituting from this equation in the previous equation,

i JEWI- i/Tfj.

Whereas the procedure discussed in connection with Fig. 1 and Fig. 2 gave a test for the constant K relation, the procedure in connection with Fig. 3 ascertains the values for only tests indirectly the network for the constant K relation, but permits an investigation of the individual members without taking the network apart. When the. reversing switch S is closed in eitherdirection, voltages are applied to the two ends of the section. These voltages are equal in magnitude and may be either in'phase or in phase opposition, accordinglto the position of the switch S If these i voltages are in phase, there will be no current in the combinations L, C, and the impedance measurement obtained by adjusting Z to et' a balance is a measurement of the two com 1- nations 1, c in parallel. Next, the reversing switch is thrown to the other position, so that the'two voltages are in opposite phase and there'is no current in the two combinations Z, a, and the adjusted value of Z to'give a balance measures the impedance of the two combinations L, C in parallel.

In Fig. 11 a network section like that of Fig. 1 is shown in a bridge arrangement that has the advantages of Fig. 1 without its disadvantage of requiring the network to be disassembled. Figs. 5* to 10 are arrangements that are auxiliary or alternative and which may be considered to lead in order to Fig. 11;

It can be shown that the network represented in Fig. 5 is equivalent to that of Fig. 1 both with respect to impedance and propagation constant over a range comprising all frequencies, with the' assumption that the capacities and inductances of Fig. -5 have the values indicated b the attached legends based oh the values in 1.

In Fig. 5 the equivalent network of Fig.

5- is connected through transformers, as

shown, to two opposite arms of a Wheatstone bridge. It is apparent that if the transformers were perfect, the arm 1418 would virtually comprise only the elements between the points 13 and 17, and the arm ll19 would virtually comprise only the condenser marked 0/2 and in parallel therewith the inductance consisting of two coils on the same core each marked Z/2 and having that inductane value alone and the two also having the mutual inductance value Z/2. In order to arrive at a modification that will be equivalent to a system with perfect transformers, I first substitute the equivalent T networks as in Fig. 6' for the transformers whose primaries are 11, 12 and 12, 19. Next, in Fig. 6, these two equivalent T networks are consolidated to one equivalent T network. In the bridge arm 2021 of Fig. 5, the transformers merely introduce apparent resistances in the path through the elements L/2 and 2C. In Fig. 7 this path is shown with the equivalent resistances introduced as R on each side.

Fig. '8 shows the proper correcting resistance K /QR introduced as compared with Fig. 6 and Fig. 9 shows the proper correcting capacities and resistances introduced-as, compared with Fig. 7. Having determined the magnitude ofthese correcting elements and introduced them by the. aid of the equivalent T network and equivalent resistances of Figs. 6 and 7, Fig. 10 is drawn, restoring the transformers, of Fig. 5, but introducing the correcting elements as shown. Fig. 10 now operates with compensated transformers. One; arm of the bridge now virtual- 1y comprises only the series combination L/2 and 2C, and the other arm of the bridge now virtually comprises only the parallel combina- I tion /2 and the coil of two parts each 1/2 having mutual inductance Z/2. Hence Fig. 10 accomplishes the balance of Fig. 1 without requiring actual disassembly of the parts 'as in Fi 1.

points and tested for the constant K relation by the bridge method. In the procedure of Fig. 11, like Fig. 10, it is not necessary to disassemble the network as was the case for Fig. l.

If the reactances of a network section such as that of Fig. 1 are not of the exact values or all of these reactances will be needful.

required, the discrepancy will be manifested as a reflection effect, and adjustment of some I have ascertained that a slight departure from the proper impedance value for any one of the four different reactances will give approximately the same resulting reflection coefficient in each case. It follows that the reflection produced by any one of these four kinds of irregularities can be compensated substantially by aisuitable change in any one of the otherv three elements. For example, suppose a lattice-type network is under construction with four elements; particular accuracy of reactance value is notnecessary for all four elements, but three of them may be approximate and then the fourth element may be putinto the combination and all the necessary corrections made by adjustment thereof to get the desired degree of accuracy in the combination.

The principle here involved is of value for I manual adjustment and may also be of value for automatic adjustment. An increase in the inductance for one pair of coils as L, L'

of Fig. 1 requires a proportional increase for the other pair, as Z, Z of Fig. 1. If the coils are subject to variation in inductance with saturation, and are made of the same kind of material and the same amount of iron and the same amount of copper, then the. change of inductance with saturation will be in the same ratio in the two kinds of coils, thus af- 'fording automatic compensation.

Iclaim: a a "1. In combination, a bridge comprising the usual four arms and two bridge members a section of lattice-type" network" forming a part of said bridge, said network having two pairs of terminals connected one way to make the network form one arm of the bridge and connected a different way to make the network form the opposite arm of the bridge,

two equal resistances forming the remaining two opposite arms of the bridge, a receiver connectedto form one of the bridging members and a source of electromotive force of a variety of frequencles connected to form the other bridging member.

2. In combination in a bridge, a constant K network with two pairs of terminals connected in one way to form one arm of the bridge and in another way to form the other arm, two equal resistances forming the remaining two arms, a receiver in one of the member, the said network having the property that when one pair of terminals are connected through a certain resistance then the input impedance across the other pair is equal to said resistance value.

4. In combination in a bridge, two transformers with their primaries in series in one arm of the bridge and with the midpoints of thesecondaries connected to the'terminals for the opposite arm, a network having two pairs of terminals, one pair connected to respective ends of the two secondaries and the other pair connected to the other ends thereof, and transformer compensating elements comprised in these connections.

5. In combination in abridge, two transformers with their primaries in series in one arm of the bridge and with the midpointsv equal resistances for the other two arms.

7. In combination in a bridge, .two transformers with their primaries in series in one arm of the bridge and with themidpoints of their secondaries connected to theterminals for the opposite arm, a network having two pairs of terminals, one pair connected t6 re spective ends of the twosecondaries and the other pair connected to the otherends thereof, transformer compensating .elements comprised in these connections, and equal resist ances forming the. remaining pair of arms of the bridge.

I The method of testing a section of network with two pairs of terminals for the constant K relation which consists in bridge balancing two resistances of value K and the network through transformers connected with the network terminals. 7

9. The method of testing a section of network having direct and across reactance combinations for the constant K relation, which consists in bridge balancing two equal resistances of value K and the impedances of the two difi'erent reactance combinations.

10. The method of testing a constant K network which consists in connecting it in a bridge in such a, way that in effect one impedance combination of the network will constitute one arm of the bridge and the other impedance combination will constitute the opposite arm.

11. In combination in a bridge, a source of electromotive force in one bridging member and a receiver in the other, resistances each of value K forming two opposite arms of the bridge, and a constant K network with its two pairs of terminals connected in the remaining two arms of the bridge so that one impedance combination of the network in effect forms one of these arms and the other impedance combination of the network in effect forms the other such arm.

In testimony whereof, I have signed my name to this specification this 23rd day of February, 1926.

HARRY NYQUIST. 

